Frailty models are widely used in multivariate survival
analysis. Two approaches are commonly used to specify the frailty model (i) the
conditional hazard (CH) and (ii) the copula (CO) approach. As they give rise to
nearly identical model expressions, the two approaches are often viewed as being
equivalent. In this paper we derive two limiting results of the positive stable
shared frailty model under CH. Our results indicate that the two model
specifications are fundamentally different and in particular, care should be
taken when modeling highly correlated survival times under CH.